Distribution of cloud fractions. Each blue line is a visualization of a cloud fraction f for a specific position angle θ. The length of each blue line represents the f value. The angle between a blue line and the positive x axis corresponds to 2θ. The radius of a black circle indicates |$\bar{f}$|⁠, or the averaged cloud fraction over all the θ bins. The red lines (which are often invisible) with a circle at the end show |$\boldsymbol{\bar{f}}$|⁠, or the averaged “cloud fraction vectors” (where the blue lines are regarded as vectors). The length of each red line (absolute value of |$\boldsymbol{\bar{f}}$|⁠) and the corresponding θ value are given in table 3. (Color online)